Borderlands – My True Vault Hunter Mode is Bugged

You only get one fresh restart of the story missions with TVHM (the same is true of normal mode).

When you played online, your game recorded how many story missions were beaten while you were present.

When you continued in 1-Player, the game asked you if you wanted to skip past the missions that you already completed online, and you said yes, you skipped ahead to the next incomplete story mission (in this case, to the end of the game, as there were none).

Also, choosing New Game only ever creates a new character. TVHM isn't (strictly speaking) a New Game, it is a different game mode that can only be started with a character that has already completed normal mode.

Yes; boss levels are treated like normal enemies levels in THVM, so as long as a boss is no longer part of a mission (meaning you've completed and handed in the mission) and you're in playthrough 2.5, the boss will scale with your level. Their loot, as always, is tied to their level, not yours, and capped at the level cap.

But effectively that means at level 50 in playthrough 2.5, repsawning bosses will be level 50(ish) and drop level 50(ish) guns. At all other times (during missions, before beating Warrior a second time) boss levels are locked in due to their mission/area levels, just like playthrough 1.